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Wyświetlanie 1-15 z 123
Tytuł:
Bounding neighbor-connectivity of Abelian Cayley graphs
Autorzy:
Doty, Lynne
Powiązania:
https://bibliotekanauki.pl/articles/743950.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Cayley graphs
neighbor-connectivity bound
Opis:
For the notion of neighbor-connectivity in graphs whenever a vertex is subverted the entire closed neighborhood of the vertex is deleted from the graph. The minimum number of vertices whose subversion results in an empty, complete, or disconnected subgraph is called the neighbor-connectivity of the graph. Gunther, Hartnell, and Nowakowski have shown that for any graph, neighbor-connectivity is bounded above by κ. Doty has sharpened that bound in abelian Cayley graphs to approximately (1/2)κ. The main result of this paper is the constructive development of an alternative, and often tighter, bound for abelian Cayley graphs through the use of an auxiliary graph determined by the generating set of the abelian Cayley graph.
Źródło:
Discussiones Mathematicae Graph Theory; 2011, 31, 3; 475-491
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Connectivity of path graphs
Autorzy:
Knor, Martin
Niepel, L'udovít
Powiązania:
https://bibliotekanauki.pl/articles/743766.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
connectivity
path graph
cycle
Opis:
We prove a necessary and sufficient condition under which a connected graph has a connected P₃-path graph. Moreover, an analogous condition for connectivity of the Pₖ-path graph of a connected graph which does not contain a cycle of length smaller than k+1 is derived.
Źródło:
Discussiones Mathematicae Graph Theory; 2000, 20, 2; 181-195
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Minimum Size of a Graph with Given Tree Connectivity
Autorzy:
Sun, Yuefang
Sheng, Bin
Jin, Zemin
Powiązania:
https://bibliotekanauki.pl/articles/32083875.pdf
Data publikacji:
2021-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
generalized connectivity
tree connectivity
eneralized k-connectivity
generalized k-edge-connectivity
packing
Opis:
For a graph $G = (V, E)$ and a set $S ⊆ V$ of at least two vertices, an $S$-tree is a such subgraph $T$ of $G$ that is a tree with $S ⊆ V(T)$. Two $S$-trees $T_1$ and $T_2$ are said to be internally disjoint if $E(T_1) ∩ E(T_2) = ∅$ and $V(T_1) ∩ V(T_2) = S$, and edge-disjoint if $E(T_1) ∩ E(T_2) = ∅$. The generalized local connectivity $κ_G(S)$ (generalized local edge-connectivity $λ_G(S)$, respectively) is the maximum number of internally disjoint (edge-disjoint, respectively) $S$-trees in $G$. For an integer $k$ with $2 ≤ k ≤ n$, the generalized $k$-connectivity (generalized $k$-edge-connectivity, respectively) is defined as $κ_k(G) = min{κ_G(S) | S ⊆ V(G), |S| = k} (λ_k(G) = min{λ_G(S) | S ⊆ V(G), |S| = k}$, respectively). Let $f(n, k, t)$ ($g(n, k, t)$, respectively) be the minimum size of a connected graph $G$ with order $n$ and $κ_k(G) = t$ ($λ_k(G) = t$, respectively), where $3 ≤ k ≤ n$ and \(1≤t≤n-⌈\frac{k}{2}⌉\). For general $k$ and $t$, Li and Mao obtained a lower bound for $g(n, k, t)$ which is tight for the case $k = 3$. We show that the bound also holds for $f(n, k, t)$ and is tight for the case $k = 3$. When t is general, we obtain upper bounds of both $f(n, k, t)$ and $g(n, k, t)$ for $k ∈ {3, 4, 5}$, and all of these bounds can be attained. When $k$ is general, we get an upper bound of $g(n, k, t)$ for $t ∈ {1, 2, 3, 4}$ and an upper bound of $f(n, k, t)$ for $t ∈ {1, 2, 3}$. Moreover, both bounds can be attained.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 2; 409-425
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the Maximum and Minimum Sizes of a Graph with Given k-Connectivity
Autorzy:
Sun, Yuefang
Powiązania:
https://bibliotekanauki.pl/articles/31341709.pdf
Data publikacji:
2017-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
k -connectivity
generalized connectivity
connectivity
Opis:
The concept of k-connectivity κk(G), introduced by Chartrand in 1984, is a generalization of the cut-version of the classical connectivity. For an integer k ≥ 2, the k-connectivity of a connected graph G with order n ≥ k is the smallest number of vertices whose removal from G produces a graph with at least k components or a graph with fewer than k vertices. In this paper, we get a sharp upper bound for the size of G with κk(G) = t, where 1 ≤ t ≤ n − k and k ≥ 3; moreover, the unique extremal graph is given. Based on this result, we get the exact values for the maximum size, denoted by g(n, k, t), of a connected graph G with order n and κk(G) = t. We also compute the exact values and bounds for another parameter f(n, k, t) which is defined as the minimum size of a connected graph G with order n and κk(G) = t, where 1 ≤ t ≤ n − k and k ≥ 3.
Źródło:
Discussiones Mathematicae Graph Theory; 2017, 37, 3; 623-632
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the connectivity of efficient point sets
Autorzy:
Song, Wen
Powiązania:
https://bibliotekanauki.pl/articles/1339089.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
vector optimization
efficient point sets
density
connectivity
Opis:
The connectivity of the efficient point set and of some proper efficient point sets in locally convex spaces is investigated.
Źródło:
Applicationes Mathematicae; 1998-1999, 25, 1; 121-127
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Edge-connectivity of strong products of graphs
Autorzy:
Bresar, Bostjan
Spacapan, Simon
Powiązania:
https://bibliotekanauki.pl/articles/743791.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
connectivity
strong product
graph product
separating set
Opis:
The strong product G₁ ⊠ G₂ of graphs G₁ and G₂ is the graph with V(G₁)×V(G₂) as the vertex set, and two distinct vertices (x₁,x₂) and (y₁,y₂) are adjacent whenever for each i ∈ {1,2} either $x_i = y_i$ or $x_i y_i ∈ E(G_i)$. In this note we show that for two connected graphs G₁ and G₂ the edge-connectivity λ (G₁ ⊠ G₂) equals min{δ(G₁ ⊠ G₂), λ(G₁)(|V(G₂)| + 2|E(G₂)|), λ(G₂)(|V(G₁)| + 2|E(G₁)|)}. In addition, we fully describe the structure of possible minimum edge cut sets in strong products of graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2007, 27, 2; 333-343
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On distance local connectivity and vertex distance colouring
Autorzy:
Holub, Přemysl
Powiązania:
https://bibliotekanauki.pl/articles/743741.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
degree condition
distance local connectivity
distance chromatic number
Opis:
In this paper, we give some sufficient conditions for distance local connectivity of a graph, and a degree condition for local connectivity of a k-connected graph with large diameter. We study some relationships between t-distance chromatic number and distance local connectivity of a graph and give an upper bound on the t-distance chromatic number of a k-connected graph with diameter d.
Źródło:
Discussiones Mathematicae Graph Theory; 2007, 27, 2; 209-227
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A topological model to assess networks connectivity and reliability
Autorzy:
Eid, M.
Hami-EL, A.
Souza de Cursi, E.
Powiązania:
https://bibliotekanauki.pl/articles/2069197.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Morski w Gdyni. Polskie Towarzystwo Bezpieczeństwa i Niezawodności
Tematy:
network
connectivity
failure
reliability
availability
Opis:
The acceleration of the interconnectivity of networks of all sorts brings to the front scene the issue of networks performance measure. Recently, one observed an accelerating course towards quantitative probabilistic models to describe and assess networks’ Connectivity, as being the main vector of performance. However, modelling realistic networks is still far from being satisfactorily achieved using quantitative probabilistic models. On the other hand, little room had been lift to exploring the potential of topological models to develop qualitative and semi- quantitative models in order to assess networks connectivity. In this paper, we are exploring the potential of the topological modelling. The proposed model is based on describing the nodepair connectivity using binary scalars of different orders (tensors). Preliminary results of our explorations sounded very promoting.
Źródło:
Journal of Polish Safety and Reliability Association; 2013, 4, 2; 167--178
2084-5316
Pojawia się w:
Journal of Polish Safety and Reliability Association
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Super-Connectivity of Kneser Graphs
Autorzy:
Ekinci, Gülnaz Boruzanli
Gauci, John Baptist
Powiązania:
https://bibliotekanauki.pl/articles/31343789.pdf
Data publikacji:
2019-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
connectivity
super-connectivity
Kneser graphs
Opis:
A vertex cut of a connected graph $G$ is a set of vertices whose deletion disconnects $G$. A connected graph $G$ is super-connected if the deletion of every minimum vertex cut of $G$ isolates a vertex. The super-connectivity is the size of the smallest vertex cut of $G$ such that each resultant component does not have an isolated vertex. The Kneser graph $KG(n, k)$ is the graph whose vertices are the $k$-subsets of ${1, 2, . . ., n}$ and two vertices are adjacent if the $k$-subsets are disjoint. We use Baranyai’s Theorem on the decompositions of complete hypergraphs to show that the Kneser graph $KG$ are super-connected when $n \ge 5$ and that their super-connectivity is \( \binom{n}{2} − 6 \) when $ n \ge 6 $.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 1; 5-11
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Kernel analysis for estimating the connectivity of a network with event sequences
Autorzy:
Tezuka, T.
Claramunt, C.
Powiązania:
https://bibliotekanauki.pl/articles/91880.pdf
Data publikacji:
2017
Wydawca:
Społeczna Akademia Nauk w Łodzi. Polskie Towarzystwo Sieci Neuronowych
Tematy:
connectivity estimation
neural network
kernel methods
spike train
Opis:
Estimating the connectivity of a network from events observed at each node has many applications. One prominent example is found in neuroscience, where spike trains (sequences of action potentials) are observed at each neuron, but the way in which these neurons are connected is unknown. This paper introduces a novel method for estimating connections between nodes using a similarity measure between sequences of event times. Specifically, a normalized positive definite kernel defined on spike trains was used. The proposed method was evaluated using synthetic and real data, by comparing with methods using transfer entropy and the Victor-Purpura distance. Synthetic data was generated using CERM (Coupled Escape-Rate Model), a model that generates various spike trains. Real data recorded from the visual cortex of an anaesthetized cat was analyzed as well. The results showed that the proposed method provides an effective way of estimating the connectivity of a network when the time sequences of events are the only available information.
Źródło:
Journal of Artificial Intelligence and Soft Computing Research; 2017, 7, 1; 17-31
2083-2567
2449-6499
Pojawia się w:
Journal of Artificial Intelligence and Soft Computing Research
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Cospectral Pairs of Regular Graphs with Different Connectivity
Autorzy:
Haemers, Willem H.
Powiązania:
https://bibliotekanauki.pl/articles/31552242.pdf
Data publikacji:
2020-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph spectrum
vertex-connectivity
edge-connectivity
spectral characterization
Opis:
For vertex- and edge-connectivity we construct infinitely many pairs of regular graphs with the same spectrum, but with different connectivity.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 2; 577-584
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
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